Momentum Calculator
Calculate momentum for two objects and the combined velocity after a collision.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Enter the two object masses and velocities. The combined velocity and energy loss assume a perfectly inelastic collision in which the objects stick together; this is a model, not a prediction for every collision.
Worked example
calculated with the default values below
Mass of object one 1,000 kg · Velocity of object one 10 m/s · Mass of object two 800 kg · Velocity of object two -5 m/s Momentum of object one 10,000.00 kg·m/s · Momentum of object two -4,000.00 kg·m/s · Total momentum 6,000.00 kg·m/s · Velocity if they stick together 3.333 m/s · Total kinetic energy 60,000.00 J · Energy lost in a stuck collision 50,000.00 J
Method and assumptions
Formula basis and scope
Linear momentum is mass × signed velocity. Combined velocity is total momentum divided by combined mass; kinetic energy loss compares initial energy with that of the combined object.
Assumes a one-dimensional perfectly inelastic collision with no external impulse. Combined velocity is not the solution for objects that rebound.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
P = m₁v₁ + m₂v₂; v′ = P ÷ (m₁ + m₂); ΔE = ½m₁v₁² + ½m₂v₂² − ½(m₁ + m₂)v′²
- P
- total momentum
- v′
- velocity after joining
- m₁, m₂
- masses
- v₁, v₂
- velocities before collision
- ΔE
- kinetic energy lost
Perfectly inelastic collision (bodies stick together); ΔE is floored at 0.
Frequently asked questions
Why does kinetic energy disappear when the two objects stick together?
The combined velocity uses conservation of momentum: 1000 times 10 plus 800 times negative 5, over 1800, equals 6000 over 1800, about 3.33 m/s for the defaults, but the final kinetic energy 0.5 times 1800 times 3.33 squared is roughly 10,000 J, far below the initial 0.5 times 1000 times 10 squared plus 0.5 times 800 times 5 squared, or 60,000 J. The missing 50,000 J is spent on heat and deformation in the perfectly inelastic collision, which is what the Energy lost output reports.